Solubility Measurement and Thermodynamic Modeling of Benzoic

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Solubility Measurement and Thermodynamic Modeling of Benzoic Acid in Monosolvents and Binary Mixtures Kadakanchi Sandeepa,†,‡ Kosuru Ravi Kumar,† Tulasi S. V. R. Neeharika,† Bankupalli Satyavathi,† and Prathap Kumar Thella*,† †

Chemical Engineering Division, CSIR-Indian Institute of Chemical Technology, Hyderabad 500007, India Academy of Scientific and Innovative Research (AcSIR), New Delhi 110001, India

‡

ABSTRACT: The solid−liquid equilibrium of benzoic acid has been determined in six monosolventstributyl phosphate, diacetone alcohol, methyl-npropyl ketone, methyl acetate, amyl acetate, and isooctaneat temperatures from 283.15 to 328.15 K and five binary systemsethanol + hexane (288.15− 328.15 K), isopropyl alcohol + hexane and chloroform + hexane (288.15− 323.15 K), acetone + hexane (288.15−318.15 K), and acetone + water (288.15−318.15 K)at atmospheric pressure with varying mole fraction of the binary mixture. The solubility was estimated by three different methods titrimetry, gravimetry, and high-pressure liquid chromatography methods. The solubility of benzoic acid was found to increase with an increase in temperature and mole fraction. Experimental solubility data was correlated with various thermodynamic models such as the Buchowski equation, the NRTL model, and the modified Apelblat−Jouyban−Acree model. The mathematical models demonstrated that the calculated and experimental solubilities of benzoic acid in the solvents were in good agreement.

1. INTRODUCTION Crystallization is one of the most important separation and purification techniques which yield a high purity of solid product with less consumption of energy compared to other separation techniques. This process is widely used in the pharmaceutical, food, microelectronic, and fine chemical industries. The two parameters temperature and type of solvent play a vital role in the crystallization process along with supersaturation, an important phenomenon for crystal nucleation and growth. The generation of supersaturation and yield of the process depends on the solubility concentration. It is necessary to have knowledge of the solubility of solids in different solvents and binary mixtures at different temperatures. The solvent also influences the rate of crystallization. Therefore, solubility data is essential for isolation of products and even for the recrystallization process. This data entails development of thermodynamic models and design of the separation process.1−3 Benzoic acid is a colorless crystalline solid. It is widely used to preserve food and beverages like fruit juice, sparkling drinks, soft drinks, and pickles. Benzoic acid and its salts are used in the manufacture of artificial flavors and perfumes and for the flavoring of tobacco. Benzoic acid is also used as an intermediate in the pharmaceutical, dye, paint, and plasticizer industries and is mainly used in the synthesis of phenol and caprolactam. Benzoic acid’s other end products including sodium and other benzoates are used for preservation and as a corrosion inhibitor.4,5 Therefore, separation and purification of benzoic acid from reaction products are important. In order to design a comprehensive and cost-effective process, it is important to have complete engineering data so as to understand the combined behavior of the solute−solvent mixture. The present work therefore details a © XXXX American Chemical Society

systematic study of the solubility of benzoic acid carried out in different solvents and in binary mixtures. Research has been carried out by many authors to study the solubility of benzoic acid in various monosolvents and binary and ternary mixtures.6−8 The solubility of benzoic acid in different monosolvents falling under the classification of acetates, ketone, alcohol, and phosphate has been reported. Thati et al.5 reported the solubility of benzoic acid in the monosolvents ethanol, chloroform, etc., and the binary mixtures such as ethanol + heptane and ethanol + toluene, in the temperature range from 278.15 to 323.15 K. Kumari et al.4 investigated the solubility of benzoic acid in acetic acid + water and acetic acid + toluene binary mixtures, and excess molar properties were also derived and various mixing rules were used to predict the refractive index values. Long et al.9 found that the solubility for benzoic acid was highest in acetone followed by 2-propanol, acetic acid, and cyclohexane. Therefore, different binary systems consisting of isopropyl alcohol, chloroform, ethanol, and acetone in hexane were chosen for the study, as these solvents are widely used for the purification of benzoic acid and they play a significant role in industrial processing. The acetone + water binary system was taken up for the study to determine the effect of the aqueous system on the solubility of benzoic acid and to interpret the water−solute interactions which lead to the low solubility.10 The authors have not come across any literature for the solubility of benzoic acid in solvents chosen for the present study. The main aim of the present study is to interpret the influence of solvent on the solubility of benzoic acid for both monosolvents Received: January 9, 2018 Accepted: May 22, 2018

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DOI: 10.1021/acs.jced.8b00025 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. List of Chemicals Used in This Work IUPAC name of chemicals (common name)

CAS registry number

source

molar mass (g·mol−1)

mass fraction purity

benzoic acid, extra pure tributyl phosphate 2,2,4-trimethylpentane (isooctane) 4-hydroxy-4-methyl-2-pentanone (diacetone alcohol) 2-pentanone (methyl-n-propyl ketone) methyl ethanoate (methyl acetate) pentyl acetate (amyl acetate) ethanol propan-2-ol (isopropyl alcohol) trichloromethane (chloroform) propan-2-one (acetone) hexane

65-85-0 126-73-8 540-84-1 123-42-2 107-87-9 79-20-9 628-63-7 64-17-5 67-63-0 67-66-3 67-64-1 110-54-3

Molychem, Mumbai, India Sigma-Aldrich, India Molychem, Mumbai, India Sigma-Aldrich, India SRL Private Limited, Mumbai, India Molychem, Mumbai, India Sigma-Aldrich, India Merck, Germany Finar, India Molychem, Mumbai, India Molychem, Mumbai, India S. D. Fine, India

122.21 266.32 114.23 116.16 86.13 74.08 130.19 46.07 60.10 119.38 58.08 86.18

≥0.995 ≥0.99 0.995 0.99 0.99 >0.99 >0.99 0.998 0.998 0.998 0.998 0.995

and binary benzoic mixtures. In this context, six monosolvents and five binary solvent mixtures were used to estimate the effect of temperature and solvent mole fractions on the solubility of acid. The experimental solubility data was analyzed by the titrimetry method, and the data was compared simultaneously with the gravimetry and HPLC methods so as to validate the applicability of the analytical methods. The experimental data was correlated using thermodynamic models, namely, the Buchowski (λh) equation, the NRTL model, and the modified Apelblat−Jouyban−Acree model (Apelblat−JA). The solubility of benzoic acid was calculated using interaction parameters obtained from the models.

with a micron filter at the tip and was used to take out the clear layer of the solution into a previously weighed measuring vial (m0), closed tightly, and weighed (m1) to verify the mass of the sample (m1 − m0). The vial was then uncorked and placed in an oven at ∼383 K for complete evaporation of solvent for 6 h. After complete evaporation of the solvent, the vial was weighed again (m2) to record the mass of the residual solid (m2 − m0).4,11 The solubility of benzoic acid in the sample solution (in mole fraction) is then calculated according to eq 1

2. EXPERIMENTAL SECTION 2.1. Materials. The details of solvents used for monosolvents and binary mixtures are described in Table 1. These solvents were stored in desiccators to prevent absorption of moisture and evaporation losses. For removal of moisture content, benzoic acid is dried in an oven for several hours until a constant weight is obtained. The purity of benzoic acid was analyzed by gas chromatography (model Shimadzu GC-2010) equipped with a flame ionization detector in a ZB-5 column having 30 m length and 0.53 mm ID, subjected to a temperature of 373.15 K initially followed by a ramping of 10 K/min up to 473.15 K. The detector and injector temperature was maintained at 423.15 K. Double distilled water used in the experiments was prepared in the laboratory, and impurities were checked by Shimadzu GC using a TCD detector. The specific conductance of the double distilled water was 1.3 μS/cm at 273.15 K. 2.2. Experimental Procedure and Solubility Measurement. The experiments were carried out in a shaking incubator (Model No. LSI-4018R) provided by Daihan Labtech India Pvt. Ltd. capable of maintaining the temperature within ±0.1 K. To carry out the solubility measurement, for each experiment, an excess amount of benzoic acid was added to 100 g of binary mixture with varying mass fractions of ethanol and hexane in Teflon-coated glass-stoppered flasks. The solutions in the flasks were continuously stirred for 9 h at constant temperature and 94.47 kPa local atmospheric pressure. The temperature of the samples was confirmed using a glass thermometer with ±0.05 K accuracy. Undissolved benzoic acid was then allowed to settle for 24 h, maintaining the same conditions of the samples. All of the experiments were carried out in duplicates, and the samples were analyzed for their solubility by the gravimetry, titrimetry, and HPLC methods. Each analysis was carried out twice, and the average value was considered for solubility estimation. 2.2.1. Gravimetry Method. A glass syringe, maintained at elevated temperature compared to that of the solution, is fitted

where x is the mole fraction solubility of benzoic acid in solvents, M1, M2, and M3 are the molecular weights of benzoic acid, ethanol, and hexane, which are 122.1, 46.07, and 86.18, respectively, and w is the mass fraction of ethanol in the solvents. 2.2.2. Titrimetric Method. The benzoic acid concentration in the saturated liquid phase of the samples was analyzed by titrimetric analysis.12 The benzoic acid concentration is determined by titrating the solution with 0.1 N NaOH in the presence of a phenolphthalein indicator. A 3 mL portion of the saturated liquid mixture was dissolved in 25 mL of neutral ethanol and was titrated against NaOH solution until the pale pink color was observed, the titer value is noted, and the mole fraction solubility of benzoic acid was determined using eq 2

x=

(m2 − m0)/M1 (m2 − m0)/M1 + (m1 − m2)w/M 2 + (m1 − m2)(1 − w)/M3

(1)

x=

(m)/M1 (m)/M1 + (b1w)/M 2 + (b1(1 − w))/M3

(2)

where m is the mass of benzoic acid present in 3 mL of saturated liquid mixture and b1 is the mass of the solvent components in 3 mL of saturated solution. 2.2.3. High Performance Liquid Chromatography. Reversedphase high-performance liquid chromatography was used to identify the concentration of benzoic acid present in saturated liquid samples as reported in the literature.13 The analysis was performed on a Shimadzu LC 20AT series high-performance liquid chromatograph equipped with a diode array detector (DAD). About 20 μL of diluted sample was injected into a reversed phase column (Luna C-18, 250 × 4.6 mm i.d., 5 μm) from phenomena. The mobile phase used was acetonitrile− phosphate buffer (by dissolving 6.8 g of potassium dihydrogen phosphate in 1000 mL of water, and the pH was adjusted to 2.3 using phosphoric acid) (35:65, v/v) for 8 min; afterward, it was then changed to acetonitrile−phosphate buffer (pH 2.3) (50:50, v/v) at a detection wavelength of 230 nm and an oven temperature 308.15 K. The calibration curve obtained from HPLC by using standard benzoic acid solutions of acid B



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concentration ranging from 20 to 200 μg/mL is as shown in Figure 1. Each sample was analyzed twice, and the average value

Figure 3. PXRD patterns of benzoic acid: (a) pure benzoic acid; (b) benzoic acid after crystallization using acetone; (c) benzoic acid after crystallization using ethanol.

Figure 1. Calibration curve of benzoic acid using HPLC.

was considered. The calibration graph was linear with an excellent regression factor of 0.99. Figure 2 represents the HPLC chromatograph of pure benzoic acid which got eluted at a retention time of 6.6−6.8 min at a corresponding wavelength of 230 nm.13 For the analysis, 25 μg of saturated liquid mixture was dissolved in 1 mL of methanol and 20 μg of the above diluted mixture was injected. The mole fraction solubility of benzoic acid was calculated using the calibration curve. 2.3. Powder X-ray Diffraction. The powder X-ray diffraction (PXRD) analysis was performed using a Bruker D8 Advanced instrument with Cu Kα radiation at 40 kV and 130 mA, to confirm the crystalline structure of the sample during the measurement. The samples were scanned in the range of 2θ = 5−70° at a scanning speed of 1°/min. 2.4. Thermodynamic Models. The modeling of experimental solid−liquid equilibrium data was explained using different thermodynamic models like the λh equation, the NRTL model, and the modified Apelblat−Jouyban−Acree model. 2.4.1. Buchowski−Ksiazczak Equation. The λh equation, also known as the Buchowski−Ksiazczak equation, is a distinguished

Figure 4. Comparison of the experimental solubility of benzoic acid in the chloroform + hexane system by gravimetry (+), titrimetry (), and the HPLC method (●).

Figure 2. HPLC chromatograph of pure benzoic acid. C



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Figure 5. Comparison of the experimental solubility of benzoic acid in (a) isopropyl alcohol (▲) and acetone (◆) and (b) ethanol (■), hexane (□), and chloroform (●) with the literature ().

Table 2. Experimental Mole Fraction Solubility of Benzoic Acid in Monosolvents at Temperatures from 283.15 to 328.15 K at 94.47 kPaa

a

temp (K)

tributyl phosphate

diacetone alcohol

methyl-n-propyl ketone

methyl acetate

amyl acetate

isooctane

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.492 0.507 0.522 0.530 0.543 0.553 0.563 0.581 0.600 0.631

0.234 0.251 0.269 0.287 0.306 0.315 0.336 0.367 0.396 0.426

0.163 0.180 0.196 0.215 0.234 0.256 0.279 0.315 0.349 0.388

0.125 0.152 0.175 0.198 0.213 0.237 0.260 0.282 0.318 0.348

0.091 0.112 0.133 0.159 0.179 0.198 0.226 0.252 0.282 0.316

0.002 0.003 0.005 0.007 0.010 0.013 0.018 0.023 0.031 0.040

Standard uncertainties u in temperature are u(T) = 0.05 K, u(P) = 0.20 kPa, and u(x) = 0.02.

nonactivity coefficient method, which was originally proposed by Buchowski et al.14,15 and is practically applicable to most solid− liquid equilibrium systems, giving excellent correlation results with just two adjustable parameters. This model approach is liable for systems having strong polarities, which incorporate strong interaction between molecules. The λh equation is given as ⎡1 ⎡ λ(1 − x) ⎤ 1 ⎤ ln⎢1 + ⎥ ⎥ = λh⎢ − ⎣ ⎦ x Tm ⎦ ⎣T

ln γ1x = −

(3)

ln γ1x = −

e

−1+λ

ΔHm ⎛ 1 1 ⎞ ⎟ ⎜ − R ⎝T Tm ⎠

(6)

The activity coefficient of solute (γ1) is given by eq 7, and the NRTL model parameters τij and Gij are evaluated using the following equations

λ λh(T −1− Tm−1)

(5)

where γ1 is the activity coefficient of solute, Tm is the melting temperature, ΔHm is the melting enthalpy, and T is the reference temperature. Equation 5 can be reduced to eq 6 by neglecting the second term, as solid−solid phase transition does not take place

Transforming eq 3 for an explicit form of x yields x=

ΔHm ⎛ 1 1 ⎞ ΔtrsH ⎛ 1 1 ⎞ ⎜ − ⎟ ⎟− ⎜ − R ⎝T Tm ⎠ R ⎝T Ttrs ⎠

(4)

where x is the molar fraction solubility at temperature T; Tm denotes the melting point of the solute. λ and h are two adjustable parameters to be determined from the solubility data. The parameter λ is approximately considered as the mean association number of solute molecules in solution which shows the nonideality of the solution system, and h estimates the enthalpy of solution. The relative deviation was considered as the objective function, and the parameter regression was carried out by minimizing the objective function. 2.4.2. Nonrandom Two-Liquid Model (NRTL). The nonrandom two-liquid model based on the activity coefficients for solid liquid equilibrium is given by eq 5

3

ln γi =

∑ j = 1 τjiGjiXj 3

∑k = 1 Gkixk

3

+

∑ j=1

3 ⎛ ∑ Xτ G ⎞ ⎜τij − k = 1 k kj kj ⎟ 3 3 ∑k = 1 Gkjxk ⎜⎝ ∑k = 1 Gkjxk ⎟⎠

XjGij

(7)

Gij = exp( −ηijτij), τij ≠ τji ,

τii = 0

τij = aij +

bij T

,

ηij = ηji , (8)

The experimental solubility data was fitted using eqs 6−8 through Matlab R2010a, to optimize the model parameters. D



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Table 3. Experimental Mole Fraction Solubility of Benzoic Acid (x) in Different Binary Mixtures with the Corresponding Mole Fraction of the First Component of the Solvent (xa) at Various Temperatures (T, K) and 94.47 kPaa ethanol + hexane xa

0

0.200

0.360

0.491

0.600

T (K)

0.772

0.840

0.900

1

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.005 0.007 0.010 0.013 0.016 0.019 0.025 0.030 0.038

0.041 0.052 0.066 0.077 0.094 0.110 0.135 0.158 0.191

0.063 0.086 0.101 0.120 0.143 0.169 0.197 0.228 0.265

0.086 0.105 0.113 0.104 0.124 0.136 0.124 0.144 0.155 0.142 0.164 0.181 0.165 0.187 0.200 0.189 0.211 0.226 0.219 0.240 0.253 0.254 0.265 0.280 0.286 0.303 0.316 isopropyl alcohol + hexane

0.136 0.163 0.179 0.197 0.216 0.240 0.266 0.292 0.319

0.153 0.171 0.188 0.209 0.227 0.249 0.270 0.300 0.325

0.157 0.179 0.196 0.215 0.235 0.255 0.280 0.304 0.328

0.154 0.165 0.178 0.194 0.216 0.232 0.253 0.274 0.293

xa

0

0.161

0.301

0.424

0.632

0.721

0.801

0.873

1

0.534

T (K)

x

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.005 0.007 0.010 0.013 0.016 0.019 0.025 0.030

0.038 0.049 0.063 0.077 0.094 0.108 0.134 0.157

0.069 0.086 0.104 0.128 0.154 0.181 0.217 0.251

0.085 0.106 0.127 0.148 0.178 0.201 0.235 0.266

0.094 0.113 0.134 0.157 0.180 0.204 0.237 0.267 chloroform + hexane

0.104 0.124 0.146 0.168 0.190 0.213 0.246 0.273

0.121 0.140 0.161 0.185 0.208 0.230 0.259 0.288

0.138 0.157 0.176 0.200 0.225 0.248 0.277 0.302

0.154 0.172 0.193 0.215 0.239 0.264 0.289 0.310

0.160 0.174 0.193 0.216 0.238 0.265 0.290 0.313

xa

0

0.154

0.291

0.413

0.523

0.622

0.711

0.793

0.868

1

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.005 0.007 0.010 0.013 0.016 0.019 0.025 0.030

0.021 0.027 0.037 0.047 0.057 0.067 0.085 0.102

0.035 0.045 0.056 0.070 0.086 0.103 0.128 0.150

0.046 0.058 0.073 0.090 0.108 0.130 0.158 0.186

0.055 0.068 0.083 0.100 0.120 0.141 0.170 0.201 acetone + hexane

0.062 0.077 0.093 0.110 0.134 0.153 0.182 0.212

0.070 0.085 0.101 0.120 0.144 0.165 0.194 0.221

0.079 0.094 0.114 0.134 0.155 0.177 0.206 0.234

0.087 0.103 0.120 0.141 0.163 0.188 0.215 0.244

0.093 0.104 0.130 0.148 0.169 0.193 0.221 0.249

xa

0

0.165

0.308

0.412

0.542

0.640

0.727

0.806

0.877

1

0.088 0.105 0.124 0.145 0.174 0.204 0.232

0.106 0.126 0.145 0.167 0.196 0.220 0.248

0.127 0.148 0.169 0.192 0.219 0.241 0.268

0.150 0.171 0.191 0.211 0.234 0.252 0.283

0.159 0.177 0.197 0.216 0.239 0.260 0.288

T (K)

x

T (K) 288.15 293.15 298.15 303.15 308.15 313.15 318.15 xa

x 0.005 0.007 0.010 0.013 0.016 0.019 0.025

0.026 0.036 0.048 0.064 0.081 0.104 0.129 0

0.051 0.063 0.079 0.095 0.118 0.136 0.166 0.057

0.060 0.074 0.091 0.112 0.138 0.166 0.193 0.094

0.074 0.090 0.108 0.132 0.157 0.185 0.210 acetone + water 0.140

0.196

T (K) 288.15 293.15 298.15 303.15 308.15 313.15 318.15 a

0.693 x

0.267

0.362

0.493

1

0.048 0.063 0.084 0.098 0.113 0.126 0.140

0.082 0.099 0.130 0.143 0.157 0.181 0.199

0.111 0.130 0.158 0.177 0.191 0.218 0.236

0.159 0.177 0.197 0.216 0.239 0.260 0.288

x 2.1 × 10−4 2.8 × 10−4 4.3 × 10−4 5.8 × 10−4 7.0 × 10−4 8.3 × 10−4 9.5 × 10−4

0.002 0.002 0.003 0.004 0.004 0.005 0.006

0.004 0.006 0.008 0.009 0.011 0.013 0.016

0.010 0.012 0.016 0.021 0.027 0.031 0.035

0.026 0.031 0.041 0.049 0.058 0.070 0.084

Standard uncertainties u in temperature are u(T) = 0.05 K, u(P) = 0.20 kPa, u(x) = 0.02, and u(xa) = 0.05. E



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Renon and Prausnitz16 proposed that the ηij value, which measures the nonrandomness in the solution correlating the solubility data, generally varies between 0.20 and 0.47; therefore, in the present study, a constant value of 0.3 was considered. In this study, ηij = ηji was also regressed. 2.4.3. Modified Apelblat−Jouyban−Acree Model. The Jouyban−Acree model can provide accurate descriptions of the solute solubility in binary solvents with respect to both temperature and solvent composition variations. The modified Apelblat equation is used to describe a nonlinear relationship between the solubility of benzoic acid in monosolvent and the reciprocal of the absolute temperature (1/T). The modified version of the Jouyban−Acree model with the modified Apelblat equation was reported to be accurate in estimating the solubility mole fractions.17,18 The combined equation could be represented as

Table 4. Buchowski−Ksiazczak Model Constants for the Solubility of Benzoic Acid in Monosolventsa λh tributyl phosphate diacetone alcohol methyl-n-propyl ketone methyl acetate amyl acetate isooctane

λ

h

100RD

−0.48 0.32 0.80 1.01 1.41 0.90

1408.72 2222.08 2050.91 2005.68 1881.66 6595.70

0.67 1.20 1.73 2.19 2.17 2.25

a

Standard uncertainties u in temperature are u(T) = 0.05 K, u(P) = 0.20 kPa, and u(x) = 0.02.

gravimetric method has been included. These results are in good agreement with the literature reports. 3.1.2. Monosolvents. The mole fraction solubility data of benzoic acid was studied in different aprotic polar solvents like tributyl phosphate, methyl-n-propyl ketone, methyl acetate, and amyl acetate, diacetone alcohol which falls under the class of protic polar solvent, and isooctane which is a nonpolar solvent, at atmospheric pressure and varying temperatures from 283.15 to 328.15 K, and the data was presented in Table 2. The solubility was found to be in the following order of tributyl phosphate > diacetone alcohol > methyl-n-propyl ketone > methyl acetate > amyl acetate > isooctane.23 It is clearly seen from the results that the solubility of benzoic acid increased with increasing temperature. The solubility of benzoic acid was found more in tributyl phosphate due to the presence of four highly electronegative oxygen atoms and one phosphorus atom which develops the formation of intermolecular hydrogen bonding, resulting in better solubility followed by diacetone alcohol which contains two oxygen atoms. Comparing the solubility in methyl acetate and amyl acetate, it is known that the number of carbon atoms increases and the nonpolarity nature increases, leading to a decrease in the solubility of benzoic acid. The solubility of benzoic acid is lowest in isooctane, as it is mono nonpolar solvent. Even comparing the dielectric constant values of the above solvents, it is clear that, as the dielectric constant increases, the polarity nature is accelerated, leading to improved solubility of benzoic acid.24 3.1.3. Binary Solvents. The solubility of benzoic acid was determined in different binary mixtures like ethanol + hexane at temperatures ranging from 288.15 to 328.15 K, isopropyl alcohol + hexane and chloroform + hexane at temperatures ranging from 288.15 to 323.15 K, acetone + hexane at temperatures ranging from 288.15 to 318.15 K, and acetone + water at temperatures ranging from 288.15 to 318.15 K and for different solvent mole fractions, and the data was tabulated in Table 3. The solubility of benzoic acid in binary mixtures containing hexane was more in ethanol followed by isopropyl alcohol, chloroform, and acetone which can be explained on the basis of the corresponding relative polarity values of the respective solvents.25 3.2. Correlation of Solubility Data Using Thermodynamic Models. The calculated mole fraction solubility of benzoic acid acquired from different thermodynamic models was used to study the relevance and precision of the models applied to the present system, and the results were examined by using the relative deviation (RD) and root-mean-square deviation (RMSD).

⎛ ⎞ ⎛ ⎞ B B ln x = xa⎜A1 + 1 + C1 ln T ⎟ + xb⎜A 2 + 2 + C2 ln T ⎟ ⎝ ⎠ ⎝ ⎠ T T N i J (xa − xb) + xaxb∑ i T (9) i=0

where the Ji terms are the Jouyban−Acree model constants and A1, B1, C1 and A2, B2, C2 are modified Apelblat model parameters obtained by correlating the experimental solubility mole fraction of benzoic acid in ethanol and hexane. xa and xb refer to the initial mole fraction of ethanol and hexane in a binary solvent mixture without solute, respectively, and N represents the number of “curve-fit” parameters.

3. RESULTS AND DISCUSSION The benzoic acid used for the study was characterized by powderXRD, and the consistent powder-XRD crystal patterns shown in Figure 3 indicated that benzoic acid did not show any phase transition even after recrystallization.19 The mole fraction solubility of the benzoic acid obtained by three analytical methods was compared, and the values were found to be comparative; therefore, all three methods were found to be reliable for solubility estimation of benzoic acid in different solvents. The mole fraction solubility of benzoic acid in monosolvents was examined by titrimetry and HPLC methods, and the binary mixtures were analyzed by the gravimetry, titrimetry, and HPLC methods. 3.1. Solubility Data. 3.1.1. Validation of Solubility Experiments.20 To validate the analytical methods and to confirm the reproducibility, all of the solubility experiments were conducted twice. The mole fraction solubility of benzoic acid in the chloroform + hexane system was determined to check the reliability of the experiment and compared with all three analytical methods which are shown in Figure 4 and represent consistency with the obtained results. The experimental solubility of benzoic acid from this work was determined and compared with data in the literature for the monosolvents as chloroform,5 hexane,21,22 isopropyl alcohol,9 acetone,9 and ethanol.5 The results of the comparison can be seen in Figure 5. The result shows a good agreement between the experimental and literature data. The relative deviation obtained for chloroform is less than 1.5% over the range of temperature. The mole fraction solubilities of benzoic acid in the solvents hexane, isopropyl alcohol, and acetone used in the present study were compared with the available literature and were observed to be in the range where the relative deviation was found to be less than 1%. Furthermore, for the solubility of benzoic acid in ethanol, as the deviation with literature data was higher in comparison to other solvents, the analysis based on the

RD = F

⎛ abs(x exp − x cal) ⎞ 1 ⎟ ∑⎜ N x exp ⎝ ⎠

(10) DOI: 10.1021/acs.jced.8b00025 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data RMSD =

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∑ (x exp − x cal)2 N

phosphate, i.e., 0.67%. On the whole, the model showed better compatibility, as the correlation results were found to have relative deviation values less than 2.25% and RMSD values of 5.15 × 10−3. The solubility in different binary mixtures was interpreted using different thermodynamic models. The model constants for the λh equation for different solvent mole fractions obtained by nonlinear regression are tabulated in Table 5 along with the corresponding relative deviation values. The graphical representation of variation by the λh equation for the isopropyl alcohol + hexane system was shown in Figure 7a. The calculated values of the chloroform + hexane system for 0.154 mole fraction from the λh equation were found to exhibit a bit more deviation of 3.01% compared to other hexane containing solvent systems. The acetone + water mixture showed higher relative deviations for the λh equation for the initial acetone + water mole fraction; i.e., for 0.057, it exhibited a maximum deviation of 7.44%, which is clearly evident from the deviation values given in Table 5, indicating that neither temperature nor mole fraction showed a significant increase in the solubility of benzoic acid. The fitted curve of the λh equation for the chloroform + hexane system is shown in Figure 7b. The NRTL model fitted well for the experimental solubility data, and the optimum temperature independent NRTL parameters are reported in Table 6. The melting temperature and enthalpy of fusion of benzoic acid used in the NRTL calculations were 395.6 K and 18.00 ± 0.01 kJ/mol.24 The maximum deviation was for the acetone + water mixture, which was 3.78%, and the smallest deviation of 0.77% was observed for the ethanol + hexane mixture, which was clearly observed in Figure 7c. The experimental solubility considering variations in both solvent mole fractions and temperatures of different binary mixtures was explained using a modified JA model, and the

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The experimental solubility of benzoic acid in monosolvents was evaluated using the λh equation, and the model constants obtained are tabulated in Table 4. The fitted curves of the Buchowski−Ksiazczak equation for monosolvents were shown in Figure 6. The maximum deviation obtained was for isooctane, i.e., 2.25%, and the minimum deviation obtained was for tributyl

Figure 6. Mole fraction solubility of benzoic acid in the monosolvents tributyl phosphate (◆), diacetone alcohol (△), methyl-n-propyl ketone (□), methyl acetate (■), amyl acetate (●), and isooctane (◇) and calculated solubilities using the Buchowski−Ksiazczak equation ().

Table 5. λh Model Constants for the Solubility of Benzoic Acid in Binary Solventsa with the Corresponding Mole Fraction of the First Component of the Solvent (xa) xa λ h 100RD

0.2 1.33 2755.10 1.26

0.36 1.99 1796.16 2.06

xa λ h 100RD

0.161 1.52 2540.37 1.96

0.301 2.51 1502.37 0.48

xa λ h 100RD

0.154 1.13 3698.87 3.01

0.291 1.59 2530.62 1.26

xa λ h 100RD

0.165 3.28 1548.58 1.17

0.308 1.83 2063.56 1.03

xa λ h 100RD a

0.057 0.06 18727.18 7.44

Ethanol + Hexane 0.6 1.19 2135.63 0.79 Isopropyl Alcohol + Hexane 0.424 0.534 2.01 1.57 1635.43 1863.96 1.29 0.85 Chloroform + Hexane 0.413 0.523 1.88 1.66 2081.29 2168.73 0.82 0.43 Acetone + Hexane 0.412 0.542 2.43 2.06 1607.03 1694.82 0.78 0.91 Acetone + Water 0.094 0.14 0.17 0.41 22996.40 9680.27 4.51 5.15 0.491 1.53 1975.27 0.81

0.693 1.22 2027.23 1.29

0.772 0.81 2349.37 1.51

0.84 0.64 2509.70 0.80

0.9 0.63 2485.36 1.02

0.632 1.44 1903.33 1.13

0.721 1.20 2003.73 0.93

0.801 1.05 2045.38 0.56

0.873 0.90 2105.18 0.63

0.622 1.56 2170.76 0.59

0.711 1.51 2134.91 0.56

0.793 1.44 2113.58 1.05

0.868 1.31 2178.76 0.18

0.64 1.91 1690.88 0.77

0.727 1.53 1821.70 0.76

0.806 1.30 1870.47 0.84

0.877 0.79 2265.61 0.97

0.196 0.72 4929.67 1.25

0.267 1.16 2836.07 5.53

0.362 1.73 1883.59 4.55

0.493 1.04 2253.91 2.59

Standard uncertainties u in temperature are u(T) = 0.05 K, u(P) = 0.20 kPa, u(x) = 0.02, and u(xa) = 0.05. G



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Figure 7. Mole fraction solubility of benzoic acid in (a) the isopropyl alcohol + hexane system and calculated solubilities using the λh equation (); (b) the chloroform + hexane system and calculated solubilities using the λh equation (); (c) the ethanol + hexane system and calculated solubilities using the NRTL model (); and (d) the ethanol + hexane system and calculated solubilities using the Apelblat−JA model ().

Table 6. NRTL Parameters and Apelblat−JA Model Constants for the Solubility of Benzoic Acid in Binary Mixturesa NRTL ethanol + hexane

100RD isopropyl alcohol + hexane

Apelblat−JA

parameter

value

parameter

value

τ12 τ21 τ31 τ13 τ23 τ32 nij

−1.01 8.07 1.05 1.58 3.22 1.95 0.3

A1 B1 C1 A2 B2 C2 J0 J1 J2

τ12 τ21 τ31 τ13 τ23 τ32 nij

0.77 −1.2 7.35 1.05 1.58 1.59 2.06 0.3

30.41 −2724.95 −4.02 175.56 −12204.66 −24.45 1270.72 −1208.46 1100.17 2.09 −0.23 −1508.05 0.64 304.81 −18014.79 −43.71 1333.62 −1533.91

H

A1 B1 C1 A2 B2 C2 J0 J1



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Table 6. continued NRTL

Apelblat−JA

parameter 100RD chloroform + hexane

100RD acetone + hexane

100RD acetone + water

value

τ12 τ21 τ31 τ13 τ23 τ32 nij

2.81 −1.03 8.67 1.05 1.58 −4.42 2 0.3

τ12 τ21 τ31 τ13 τ23 τ32 nij

3.24 −1.42 4.18 1.05 1.58 9.38 1.49 0.3

τ12 τ21 τ31 τ13 τ23 τ32 nij

2.1 −1.42 4.18 6.17 221.05 0.33 5.18 0.3

100RD a

parameter

value

J2

1483.97 1.40 −12.72 −1716.72 2.88 375.65 −21243.65 −54.25 1051.43 −1114.43 978.59 2.67 −24.65 −487.51 4.33 356.68 −20742.33 −51.21 1064.78 −1186.30 1414.73 2.45 −67.99 1490.56 10.77 884.27 −44444.38 −130.40 3377.52 −3053.11 3183.16 3.36

A1 B1 C1 A2 B2 C2 J0 J1 J2 A1 B1 C1 A2 B2 C2 J0 J1 J2 A1 B1 C1 A2 B2 C2 J0 J1 J2

3.33

Standard uncertainties u in temperature are u(T) = 0.05 K, u(P) = 0.20 kPa, u(x) = 0.02, and u(xa) = 0.05.

relative constants and deviations are given in Table 6. The fitted values for the Apelblat−JA model are shown in Figure 7d for the ethanol + hexane binary mixture. The calculated mole fraction solubilities of benzoic acid for the ethanol + hexane system were found to be in harmony with the experimental results which were depicted in the RD values of 2.09% and RMSD deviation value of 4.15 × 10−3. For the acetone + water system, the Apelblat−JA model shows a bit more deviations at lower temperatures and lower solvent fractions. This behavior may be due to the fact that benzoic acid consists of a benzene ring and a carboxylic acid group which has a poor solubility in water.26

greater in the ethanol + hexane mixture and minimum in the acetone + water system and in particular at lower mole fraction shows poor solubility. It can be seen that the predicted and experimental solubilities of benzoic acid are in qualitatively good compatibility for the considered solvents which are reflected in the RD values. The Buchowski equation exhibited low percentage relative deviation values of 0.67% for tributyl phosphate. The ethanol + hexane system exhibits the least deviation of 0.77% for the NRTL model. The Apelblat−JA model was proportionate enough to explain the solubility of isopropyl alcohol + hexane which shows a slight RD value of 1.40%.

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4. CONCLUSIONS In the present study, the solubility of benzoic acid was estimated in six monosolvents from 283.15 to 328.15 K and in five binary solvent mixtures by varying temperatures and mole fractions. All three analytical methods applied to estimate solubility have given proportionate results. The solubility of benzoic acid for monosolvent systems was found to be more in tributyl phosphate and lowest in isooctane, which might be due to the fact that, as the dielectric constant value decreases, the solubility of benzoic acid decreases and it increases with an increase in temperature. The solubility of benzoic acid was found to be increasing with an increase in temperature and mole fraction; in the binary mixtures studied, it was observed that the solubility of benzoic acid was

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Bankupalli Satyavathi: 0000-0002-8495-317X Notes

The authors declare no competing financial interest.

■

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Solubility Measurement and Thermodynamic Modeling of Benzoic

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